This problem
plays an important role in many fields,
such as equilibrium problems, fixed point problems, variational inequalities, and composite minimization problems, see, for example, [1]}, [2]}, [3]}. To be more precise, many
problems in signal processing,
computer vision and machine learning
can be modeled mathematically as this formulation, see [4]}, [5]}, [6]} and the references therein. For solving the problem (REF ), the so-called forward-backward splitting method
is given as follows:
\(x_{n+1}=(I+\lambda A)^{-1}(x_n-\lambda Bx_n),\) 
